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I’m currently writing a personal statement for a PhD application I am putting together and I have the sentence, “Not to be overly dramatic, but when I saw the advertisement for this project I breathed a sigh of relief because...”
I’m wondering whether this sentence is a bit too embellished and casual to have here, because in the past I’ve been told that a personal statement shouldn’t be too formal but it shouldn’t be too casual either.
That sentence already sounds very flippant. Contrary to its name there is very little that is "personal" about a personal statement (and it's definitely not the kind of soul-searching essay you write for college). It's mostly a document to describe your research experience and how the program fits within your vision of a scientific career. You should certainly demonstrate your interest and passion (in a concrete manner devoid of cliches, of course), but I'd rather err on the side of being too formal than the other way around.
The issue with that sentence is not that it's too casual, but that it's devoid of relevant content. Personal statements (like all academic writing) should be as factual as possible, and the facts should help the committee determine whether or not you would be a good candidate. That is an academic decision (are you strong enough and independent enough, are your interests a good fit for the department, e.g. is there a suitable advisor, etc.), not an emotional one (whether or not you would be a good buddy to hang out with in the evenings is, ideally, not part of the considerations). The people reading these statements are busy, they typically have to read a number of these, and teach, do research, and discharge other administrative duties the rest of the time, so you will help them by keeping your letter to the point. Waffle, whether in research papers or in personal statements, is annoying because it wastes time.
Note that there is no contradiction between being factual and being personal: statements about your academic and other related experience (e.g. relevant jobs and work placements, olympiads, etc), about the courses you have taken, about the courses you found most interesting, about the possible directions that you think you might want to take your research, and so on are relevant; dramatic descriptions of your emotions at a particular point in time are not.
I'd say that's too casual. I agree with the previous answer that it's best to err on the formal side. Something more like: "The XXX element of this project particularly excites me because..." would be more appropriate - it's good to be personal, but keep a measured tone. You can demonstrate your enthusiasm for the project by being specific about why it suits you and vice versa.
